The distribution of the sum-of-digits function

Michael Drmota; Johannes Gajdosik

Displaying similar documents to “The distribution of the sum-of-digits function”

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

Applicationes Mathematicae

Similarity:

The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].

Limitation to the asymptotic formula in Waring's problem

W. K. A. Loh (1996)

Acta Arithmetica

Similarity:

On the discrepancy of (nα)

Johannes Schoißengeier (1984)

Acta Arithmetica

Similarity:

On partitions without small parts

J.-L. Nicolas, A. Sárközy (2000)

Journal de théorie des nombres de Bordeaux

Similarity:

Let $r (n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$ . By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$ , which holds for $n \to \infty$ , and $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .

The renewal theorem for random walk in two-dimensional time

P. Ney, S. Wainger (1972)

Studia Mathematica

Similarity:

The discrepancy of random sequences {kx}

H. Kesten (1964)

Acta Arithmetica

Similarity:

Irrational rapidly convergent series

Jaroslav Hančl (2002)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

On power series with only finitely many coefficients(mod 1): Solution of a problem of Pisot and Salem

David Cantor (1977)

Acta Arithmetica

Similarity:

On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

Let $q, q_{1}, \dots, q_{s} \geq 2$ be integers, and let $α_{1}, α_{2}, \dots$ be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence ${(\{α_{m} q^{n}\}, \dots, \{α_{m + s - 1} q^{n}\})}_{m, n = 1}^{M N}$ coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences ${(x n)}_{n = 1}^{M N}$ in $s$ -dimensional unit cube $(s, M, N = 1, 2, \dots)$ . We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence ${(\{α_{1} q_{1}^{n}\}, \dots, \{α_{s} q_{s}^{n}\})}_{n = 1}^{N}$ (Korobov’s problem).

On mean central limit theorems for stationary sequences

Jérôme Dedecker, Emmanuel Rio (2008)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In this paper, we give estimates of the minimal $𝕃^{1}$ distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.